Question

the lengths of a triangle are given below. is the the triangle obtuse, acute, or right? 4, 5, 6

Explanation:

Step1: Identify the longest side

The sides of the triangle are \(4\), \(5\), \(6\). The longest side \(c = 6\).

Step2: Apply the Pythagorean - related inequality

For a triangle with sides \(a\), \(b\), \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}>c^{2}\), the triangle is acute; if \(a^{2}+b^{2}=c^{2}\), the triangle is right - angled; if \(a^{2}+b^{2}Let \(a = 4\) and \(b = 5\). Then \(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25=41\), and \(c^{2}=6^{2}=36\).
Since \(41>36\) (i.e., \(a^{2}+b^{2}>c^{2}\)).

Answer:

acute